G150 ARR TO FFZ ON P50 FREQ EXPERIENCED TCAS RA AT 4000 FT IN IMC CONDITIONS; NO TFC ISSUED; NO OPERROR RECORDED.

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I WAS ON A RADAR VECTOR FOR AN APCH INTO MESA; AZ (FFZ). I WAS HDG S I BELIEVE ON A 180 DEG HDG. I WAS TOLD TO DSND TO 4000 FT MSL. SHORTLY AFTER LEVELING AT 4000 FT; I RECEIVED AN RA TO DSND. WE IMMEDIATELY DSNDED FOLLOWING OUR COMMAND BARS. WHILE THE RA WAS SOUNDING IN OUR HEADSETS AND WE WERE DSNDING; WE ADVISED ATC OF OUR RA DEV. WE EVENTUALLY REACHED AROUND 3400 FT MSL. I WAS VERY CONCERNED WITH TERRAIN IN THE AREA; CONSIDERING I WAS IMC AT THIS TIME AND NUMEROUS MOUNTAIN PEAKS IN THE AREA. WE WERE TURNED E BY ATC INSTRUCTION. ONCE THE RA WAS RESOLVED; I TURNED AND STARTED CLBING BACK UP TO 4000 FT PER ATC INSTRUCTIONS. ONCE LEVEL AT 4000 FT FOR A SHORT PERIOD; ABOUT 1 OR 2 MINS; I WAS TOLD TO IMMEDIATELY CLB TO 5000 FT FOR TFC. NO RA THIS TIME; BUT A TA. I STARTED THE CLB IMMEDIATELY WITH FULL PWR AND DURING THE CLB UP I WAS TOLD THE TFC CONFLICT WAS RESOLVED AND DSND BACK DOWN TO 4000 FT. I WAS GIVEN ANOTHER HDG FOR MESA AND THEN EVENTUALLY CLRED FOR THE VISUAL. IN THE PAST YR I HAVE RECEIVED 3 OTHER RA'S GOING INTO AND OUT OF BOTH SCOTTSDALE AND MESA. IT SEEMS TO ME THIS IS VERY EXCESSIVE; CONSIDERING I HAVE NEVER HAD ANOTHER RA ANYWHERE ELSE IN THE UNITED STATES. A PHOENIX CTLR HAS MENTIONED TO ME IN THE PAST THAT THE TWRS OF THE OTHER ARPTS ARE SENDING TFC INTO THEIR ARR AND DEP PATHS. I WOULD BELIEVE THERE NEEDS TO BE BETTER COM AND PRACTICES BTWN THE TWRS OF THE OUTLYING ARPTS AND PHOENIX APCH CTL. I BELIEVE THE FIRST RA WAS A CTLR FAULT OF SIMPLY NOT SEEING THE CONFLICT. TFC WAS HVY AND WX IN PHOENIX CAUSED EXCESSIVE WORKLOAD ON THE CTLRS. THE SECOND CONFLICT; I BELIEVE; WAS CAUSED FROM BOTH BAD CTLR INSTRUCTIONS AND SEPARATION; AND HVY WORKLOAD ON ME FROM TRYING TO DEAL WITH GETTING THE PLANE BACK INTO A STRAIGHT AND LEVEL SITUATION FOLLOWING THE RAPID DSCNT FROM THE RA. I HAD TO STOP THE DSCNT; CLB BACK TO 4000 FT AND TURN -- ALL WHILE DEALING WITH WHERE TERRAIN WAS; OTHER TFC; AND CHANGING THE ATTITUDE OF THE PLANE. IT IS SIMPLY A PERFECT EXAMPLE OF THE ERROR CHAIN OF EVENTS ACCIDENT. FIRST THE RA; THE HVY WORKLOAD BOTH ON PLT AND CTLR; NUMEROUS TURNS; A DSCNT; FOLLOWED BY A LEVELOFF; THEN FOLLOWED BY AN IMMEDIATE CLB. MY FO WAS DOING ALL THE TALKING TO ATC; AND I WAS FLYING. IT WAS HARD TO HEAR INSTRUCTIONS FROM ATC FROM THE NUMEROUS RA CALLOUTS OF THE AIRPLANE AND TA CALLOUTS WHICH WERE SHOUTING QUITE LOUD IN OUR HEADSETS -- WHICH MADE IT DIFFICULT TO UNDERSTAND THE INSTRUCTIONS GIVEN. THERE WAS NEVER ANY INDICATION OF PLT FAULT FROM THE CTLR; AND WHEN HANDED OFF TO MESA TWR WE WERE TOLD 'THANKS FOR YOUR HELP.' THIS EVENT MADE BOTH MYSELF; CO-PLT; AND PAX UNCOMFORTABLE FROM THE NUMEROUS AMOUNT OF ACTIVITY THAT TOOK PLACE IN SUCH A SHORT PERIOD. BOTH PLTS AND CTLRS WERE OBVIOUSLY OVERLOADED DURING THE WHOLE SITUATION; WHICH LED TO NUMEROUS MISTAKES.